New space–time spectral and structured spectral element methods for high order problems
We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space a...
Ausführliche Beschreibung
Autor*in: |
Zhang, Chao [verfasserIn] Yao, Hanfeng [verfasserIn] Li, Huiyuan [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2018 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Journal of computational and applied mathematics - Amsterdam [u.a.] : North-Holland, 1975, 351, Seite 153-166 |
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Übergeordnetes Werk: |
volume:351 ; pages:153-166 |
DOI / URN: |
10.1016/j.cam.2018.08.038 |
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Katalog-ID: |
ELV001293257 |
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100 | 1 | |a Zhang, Chao |e verfasserin |4 aut | |
245 | 1 | 0 | |a New space–time spectral and structured spectral element methods for high order problems |
264 | 1 | |c 2018 | |
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520 | |a We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. | ||
650 | 4 | |a Space–time spectral method | |
650 | 4 | |a Dual-Petrov–Galerkin | |
650 | 4 | |a Structured spectral element method | |
700 | 1 | |a Yao, Hanfeng |e verfasserin |4 aut | |
700 | 1 | |a Li, Huiyuan |e verfasserin |0 (orcid)0000-0002-6326-9926 |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Journal of computational and applied mathematics |d Amsterdam [u.a.] : North-Holland, 1975 |g 351, Seite 153-166 |h Online-Ressource |w (DE-627)266889204 |w (DE-600)1468806-2 |w (DE-576)075962373 |7 nnns |
773 | 1 | 8 | |g volume:351 |g pages:153-166 |
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936 | b | k | |a 31.00 |j Mathematik: Allgemeines |
951 | |a AR | ||
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31.00 |
publishDate |
2018 |
allfields |
10.1016/j.cam.2018.08.038 doi (DE-627)ELV001293257 (ELSEVIER)S0377-0427(18)30525-9 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Zhang, Chao verfasserin aut New space–time spectral and structured spectral element methods for high order problems 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. Space–time spectral method Dual-Petrov–Galerkin Structured spectral element method Yao, Hanfeng verfasserin aut Li, Huiyuan verfasserin (orcid)0000-0002-6326-9926 aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 351, Seite 153-166 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:351 pages:153-166 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 351 153-166 |
spelling |
10.1016/j.cam.2018.08.038 doi (DE-627)ELV001293257 (ELSEVIER)S0377-0427(18)30525-9 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Zhang, Chao verfasserin aut New space–time spectral and structured spectral element methods for high order problems 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. Space–time spectral method Dual-Petrov–Galerkin Structured spectral element method Yao, Hanfeng verfasserin aut Li, Huiyuan verfasserin (orcid)0000-0002-6326-9926 aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 351, Seite 153-166 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:351 pages:153-166 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 351 153-166 |
allfields_unstemmed |
10.1016/j.cam.2018.08.038 doi (DE-627)ELV001293257 (ELSEVIER)S0377-0427(18)30525-9 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Zhang, Chao verfasserin aut New space–time spectral and structured spectral element methods for high order problems 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. Space–time spectral method Dual-Petrov–Galerkin Structured spectral element method Yao, Hanfeng verfasserin aut Li, Huiyuan verfasserin (orcid)0000-0002-6326-9926 aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 351, Seite 153-166 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:351 pages:153-166 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 351 153-166 |
allfieldsGer |
10.1016/j.cam.2018.08.038 doi (DE-627)ELV001293257 (ELSEVIER)S0377-0427(18)30525-9 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Zhang, Chao verfasserin aut New space–time spectral and structured spectral element methods for high order problems 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. Space–time spectral method Dual-Petrov–Galerkin Structured spectral element method Yao, Hanfeng verfasserin aut Li, Huiyuan verfasserin (orcid)0000-0002-6326-9926 aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 351, Seite 153-166 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:351 pages:153-166 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 351 153-166 |
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10.1016/j.cam.2018.08.038 doi (DE-627)ELV001293257 (ELSEVIER)S0377-0427(18)30525-9 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Zhang, Chao verfasserin aut New space–time spectral and structured spectral element methods for high order problems 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. Space–time spectral method Dual-Petrov–Galerkin Structured spectral element method Yao, Hanfeng verfasserin aut Li, Huiyuan verfasserin (orcid)0000-0002-6326-9926 aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 351, Seite 153-166 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:351 pages:153-166 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 351 153-166 |
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New space–time spectral and structured spectral element methods for high order problems |
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New space–time spectral and structured spectral element methods for high order problems |
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Zhang, Chao |
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Journal of computational and applied mathematics |
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Journal of computational and applied mathematics |
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Zhang, Chao Yao, Hanfeng Li, Huiyuan |
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10.1016/j.cam.2018.08.038 |
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new space–time spectral and structured spectral element methods for high order problems |
title_auth |
New space–time spectral and structured spectral element methods for high order problems |
abstract |
We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. |
abstractGer |
We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. |
abstract_unstemmed |
We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C 1 -conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations. |
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title_short |
New space–time spectral and structured spectral element methods for high order problems |
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